A shopping mall has a large basement parking lot with parking slots painted in it along a single row. These slots are quite narrow; a compact car can fit in a single slot but an SUV requires two slots. When a car arrives, the parking attendant guides the car to the first available slot from the beginning of the row into which the car can fit. For our purpose, cars are numbered according to the order in which they arrive at the lot. For example, the first car to arrive is given a number 1, the second a number 2, and so on. This numbering does not indicate whether a car is a compact or an SUV. The configuration of a parking lot is a sequence of the car numbers in each slot. Each single vacant slot is represented by letter V.
For instance, suppose cars numbered 1 through 5 arrive and park, where cars 1, 3 and 5 are compact cars and 2 and 4 are SUVs. At this point, the parking lot would be described by the sequence 1, 2, 3, 4, 5. If cars 2 and 5 now vacate their slots, the parking lot would now be described as 1, V, V, 3, 4. If a compact car (numbered 6) arrives subsequently followed by an SUV (numbered 7), the parking lot would be described by the sequence 1, 6, V, 3, 4, 7. Answer the following questions INDEPENDENTLY of each other.
Q. 1 Initially cars numbered 1, 2, 3, and 4 arrive among which 1 and 4 are SUVs while 2 and 3 are compact cars. Car 1 then leaves, followed by the arrivals of car 5 (a compact car) and car 6 (an SUV). Car 4 then leaves. Then car 7 (an SUV) and car 8 (a compact car) arrive. At this moment, which among the following numbered car is parked next to car 3?
1) 6
2) 5
3) 8
4) 7
Explanation
Correct Answer
4
Explanation
According to the question, cars 1, 4, 6 and 7 are SUVs and cars 2, 3, 5 and 8 are compact cars. Now, their arrival and departure are described in the following steps.
I. 1, 2, 3, 4
II. V, V, 2, 3, 4
III. 5, V, 2, 3, 4
IV. 5, V, 2, 3, 4, 6
V. 5, V, 2, 3, V, V, 6
VI. 5, V, 2, 3, 7, 6
VII. 5, 8, 2, 3, 7, 6
Clearly, car 7 is parked next to car 3.
Q. 2 Suppose eight cars have arrived, of which two have left. Also suppose that car 4 is a compact and car 7 is an SUV. Which of the following is a POSSIBLE current configuration of the parking lot?
1) V, 2, 3, 7, 5, 6, 8
2) 8, 2, 3, V, 6, 5, 7
3) 8, 2, 3, V, 5, 7, 6
4) 8, 2, 3, V, 5, 6, 7
Explanation
Correct Answer
4
Explanation
Option 1 is not possible as car 7 cannot be parked between car 3 and car 5 because car 7 is an SUV.
Option 2 is not possible as car 6 cannot be parked just before car 5 because 4th slot is vacant and car 4 is a compact car. Option 3 is also not possible as car 7 which is an SUV cannot be parked between car 5 and car 6.
Option 4 is the possible current configuration of the parking lot (Car 1 and car 4 have left and in place of car 1, car 8 then arrived in that slot)
Q. 3 Suppose the sequence at some point of time is 4, 5, 6, V, 3. Which of the following is NOT necessarily true?
1) Car 1 is an SUV.
2) Car 5 is a compact.
3) Car 4 is a compact.
4) Car 3 is an SUV.
Explanation
Correct Answer
4
Explanation
Seeing the sequence: 4, 5, 6, V, 3, we can conclude that car 1 and car 2 are definitely SUVs which occupied two slots each. After that car 4, car 5 and car 6 arrived and one slot is vacant which clearly means car 4 and car 5 are compact cars. We cannot say about the type of car 3 so option 4 is not necessarily true.
Q. 4 Suppose that car 4 is not the first car to leave and that the sequence at a time between the arrival of the car 7 and car 8 is V, 7, 3, 6, 5. Then which of the following statements MUST be false?
1) Car 2 is a compact.
2) Car 7 is a compact.
3) Car 4 is an SUV.
4) Car 6 is a compact.
Explanation
Correct Answer
4
Explanation
